For the even parity ground state, the Berry curvature \(\Omega (k)\)  is plotted in Fig. REF (a) for \(N=15\) 
with a stacking fault at the center \((m,n) = (8,8)\) . This plot can be interpreted as the superposition of contributions from two identical sections of RMG summing to give a single peak. By contrast, Fig. REF (b) shows \(\Omega (k)\)  for the even parity ground state with the stacking fault off-center \((m,n) = (12,4)\) . In this case, there are two separate peaks corresponding to the sections of length \(m=12\)  and \(n=4\) . For both of these cases, the Berry curvature \(\Omega (k)\)  sums to give a Chern number of magnitude \(N/2\)  [1]}, [2]}, [3]}.
Although these are even parity states, they give the same Chern numbers as the odd parity states in the system with a Bernal fault. The reason is that the twin boundary fault effectively flips the position of \(A\)  and \(B\)  sites within a layer for the layers above the fault (right panel of Fig. REF ) compensating the change of relative sign of potential differences for the even parity state.
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